Beyond halfway to Hadwiger's conjecture

Abstract

Hadwiger conjectured in 1943 that every graph with no $K_t$ minor has chromatic number at most $t-1$. Delcourt and Postle proved that every graph with no $K_t$ minor has chromatic number $O(t\log\log t)$. We build on their result to improve this bound to $O(t\log\log\log t)$.